As it happens, the applicability of the slow-roll condition is closely
connected to the condition for inflation to take place, and in many
contexts the conditions can be regarded as equivalent. Let's quickly see
why.

The inflationary condition
> 0 is satisfied for a much wider
range of behaviours than just (quasi-)exponential expansion. A classic
example is power-law inflation
atp for p > 1, which is an exact
solution for an exponential potential

(45)

We can manipulate the condition for inflation as

where the last manipulation uses the slow-roll approximation. The final
condition is just the slow-roll condition
< 1, and hence

Inflation will occur when the slow-roll conditions are satisfied (subject
to some caveats on whether the `attractor' behaviour has been
attained. [5])

However, the converse is not strictly true, since we had to use the
SRA in the derivation. However, in practice

The last condition arises because unless the curvature of the potential
is small, the potential will not be flat for a wide enough range of
.